H.J. Trussell

Mathematics for demosaicking

Digital color cameras sample the continuous color spectrum using three or more filters; however, each pixel represents a sample of only one of the color bands. This arrangement is called a mosaic. To produce a full-resolution color image, the recorded image must be processed to estimate the values of the pixels for all the other color bands. This restoration process is often called demosaicking. This paper uses stacked notation to represent the mosaicked image capture and derives the minimum mean square error (MMSE) estimator for the demosaicked image. By making common assumptions, the restoration can be computed in a cost-effective manner. Extensions to the linear method are proposed to allow adaptive behavior.

Filter considerations in color correction

The quality of color correction is dependent on the filters used to scan the image. This paper introduces a method of selecting the color filters using a priori information about the viewing illuminants. Color correction results using the derived filters are compared with color correction results using filters that are optimal for individual viewing and recording illuminants. The comparison is performed using the CIE PEL (L*a*b*) perceptual color difference measure. Applications of this work are found in the design of scanners, copiers, and television systems.

Figures of merit for color scanners

In the design and evaluation of color scanners and cameras, it is useful to have a single figure of merit that closely agrees with perceived color accuracy. In the past, several measures of goodness for color scanning filters have been proposed to fulfil such a requirement. Most of the proposed measures have had shortcomings in that they are either based on error metrics in color spaces that are not perceptually uniform, or in that they do not take into account the effects of measurement noise. An extension of the most promising measure, based on linearized CIELAB space, is proposed to obtain a new figure of merit that has a high degree of perceptual relevance and also accounts for the varying noise performance of different filters. The paper also provides a common framework for the different figures of merit and a comprehensive comparison of their computational complexity and reliability.

Color imaging for multimedia

To a significant degree, multimedia applications derive their effectiveness from the use of color graphics, images, and video. However, the requirements for accurate color reproduction and for the preservation of this information across display and print devices that have very different characteristics and may be geographically apart are often not clearly understood. This paper describes the basics of color science, color input and output devices, color management, and calibration that help in defining and meeting these requirements.

Mathematical methods for the design of color scanning filters

The problem of the design of color scanning filters is addressed in this paper. The problem is posed within the framework of the vector space approach to color systems. The measure of the goodness of a set of color scanning filters presented in earlier work is used as an optimization criterion to design color scanning filters modeled in terms of known, smooth, nonnegative functions. The best filters are then trimmed using the gradient of the mean square DeltaE(ab) error to obtain filters with a lower value of perceptual error. The results obtained demonstrate the utility of the method.

Color image generation and display technologies

The goal of this article is to provide an overview of the transformations and limitations that occur in color imaging input and output devices. We concentrate on two common recording devices and three common output devices. First we provide an overview of digital scanners and cameras, and then we discuss inkjet and laser printers. Finally, liquid crystal display (LCD) devices are presented.

Optimal nonnegative color scanning filters

In this correspondence, the problem of designing color scanning filters for multi-illuminant color recording is considered. The filter transmittances are determined from a minimum-mean-squared orthogonal tristimulus error criterion that minimizes the color error in estimates obtained from noisy recorded data. Nonnegativity constraints essential for physical realizability are imposed on the filter transmittances. In order to demonstrate the significant improvements obtained, the resulting filters are compared with suboptimal filters reported in earlier literature.

Processing of X-ray images

A review of three aspects of image processing of X-ray imagery is presented. Short reviews of computer assisted tomography and coded aperture imaging are given. The application of image enhancement and restoration to radiography is reviewed in greater depth.

Colorimetric restoration of digital images

A colorimetric approach to restoration of digital images is presented. Assumptions are made to simplify the general problem to obtain a more computable form. Two methods are developed, using Karhunen-Loeve transformation and independent restoration schemes from earlier works, to solve the estimation problem in color image processing using multidimensional restoration. A comparison of the methods is presented including the effects of parameters of interest to desktop scanners and digital cameras. The results for the SNRs and blurs studied indicate that more than three color channels produces a slight numerical gain and modest visual gain.

Set theoretic signal restoration using an error in variables criterion

The restoration of a signal degraded by a stochastic impulse response is formulated as a problem with uncertainties in both the measurements and the impulse response. The method of total least squares, and variants thereof, are effective techniques for solving this class of problems. However, unlike set theoretic estimation schemes, these methods do not allow the incorporation of other a priori information in the estimate. In this correspondence, two new sets motivated by total least squares are introduced for set theoretic estimation. The convexity of these sets is established and the projection operators onto these sets are given. Through simulations, the advantages of the new technique over conventional and older set theoretic schemes for restoration are demonstrated.